Question

The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.

Company A

34	59	43	30	3
32	42	85	30	48
110	50	10	26	70
52	83	78	27	70
27	90	38	52	76

Company B

44	64	41	32	65
104	45	27	37	84
76	45	34	51	63
43	34	32	63	66

(a)

Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let μ₁ = population mean minutes late for delayed Company A flights and μ₂ = population mean minutes late for delayed Company B flights.)

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

     

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

(b)

What is the sample mean number of minutes late for delayed flights for each of these two airlines?

Company A  minCompany B  min

(c)

Calculate the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Reject H₀. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.Do not reject H₀. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.     Do not Reject H₀. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.Reject H₀. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

Answer 1

	A	B	(A-A_bar)^2	(B-B_bar)^2
	34	44	275.56	72.25
	59	64	70.56	132.25
	43	41	57.76	132.25
	30	32	424.36	420.25
	3	65	2265.76	156.25
	32	104	345.96	2652.25
	42	45	73.96	56.25
	85	27	1183.36	650.25
	30	37	424.36	240.25
	48	84	6.76	992.25
	110	76	3528.36	552.25
	50	45	0.36	56.25
	10	34	1648.36	342.25
	26	51	605.16	2.25
	70	63	376.36	110.25
	52	43	1.96	90.25
	83	34	1049.76	342.25
	78	32	750.76	420.25
	27	63	556.96	110.25
	70	66	376.36	182.25
	27		556.96
	90		1552.36
	38		158.76
	52		1.96
	76		645.16
Total	1265	1050	16938	7713
	A_bar	B_bar
mean	50.6	52.5
n	25	20
	S1	S2
SD	26.56596	20.14814

Sample means:

	A_bar	B_bar
mean	50.6 min	52.5 min

Hypothesis:

H0: μ1 − μ2 = 0

V/s

Ha: μ1 − μ2 ≠ 0

under Ho,

(assuming equal variances)

Where,Pooled Standard deviation,

Decision : If p-value < alpha then we reject Ho.

Calculation :

DF = 43

WE find p-value using Excel

=T.DIST.2T(0.265,43)

=0.7923

At 0.05 level level of significance

p-value = 0.7923 > alpha = 0.05 then we fail to reject Ho.

Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.